Muon/Muonium in an Isotopically Pure 13C Diamond

A preliminary study of the diamagnetic (μ_d) and the paramagnetic (Mu _T ) states in a synthetic ¹³C diamond has been performed using the Transverse Field Muon Spin Rotation method. This system could be used to verify the quantum diffusion behaviour observed before, however, with a more reliable extraction of the hopping rate. The results were obtained in an applied magnetic field of 7.5 mT and at sample temperatures of 10 K, 100 K and 200 K. The prompt fraction, f, of the μ_d state remains constant at 22(5)% in the range 10–200 K; that of the Mu _T state increases from 53(10)% at 10 K to 78(10)% at 200 K. The fractions of the two states add to 100% at 200 K, suggesting non-population of the bond-centred state, Mu_BC, which is often observed in other diamond samples. The μ_d state has a spin relaxation rate of 0.20(5) μs⁻¹, in contrast to the zero value obtained in type II diamond samples. This indicates appreciable interaction of the μ_d state with the ¹³C atoms. The Mu _T state has a large spin relaxation rate ranging from 3.0(5) μs⁻¹ at 10 K to 7.0(5) μs⁻¹ at 200 K, consistent with values obtained in diamond samples with defects. This work is part of ongoing studies of muon/muonium-defect interactions in diamonds. This revised version was published online in September 2006 with corrections to the Cover Date.     

Muonium states in silicon carbide

Implanted muons in samples of silicon carbide have been observed to form paramagnetic muonium centers (μ ⁺ e⁻). Muonium precession signals in low applied magnetic fields have been observed at 22 K in a granular sample of cubic β-SiC, however it was not possible to determine the hyperfine frequency. In a single crystal sample of hexagonal 6H-SiC, three apparently isotropic muonium states were observed at 20 K and two at 300 K, all with hyperfine frequencies intermediate between those of the isotropic muonium centers in diamond and silicon. No evidence was seen of an anisotropic muonium state analogous to the Mu^* state in diamond and silicon.     

Diffusion, trapping, and relaxation of Mu+ and Mu- in heavily‐doped GaAs

The diamagnetic muonium states in heavily doped GaAs are investigated with a combination of transverse‐field and longitudinal‐field μSR techniques. In metallic n‐type GaAs, formation of Mu^- occurs because of the high Fermi energy. This analog of the hydride ion (H^-) is located in a T_Ga interstice where it is essentially immobile up to about 500 K. At higher temperatures, Mu_T acts as an electron–hole recombination center. In p‐type GaAs, Mu⁺ traps at two different sites, one at low temperatures and a second at higher temperatures after detrapping from the first. This revised version was published online in August 2006 with corrections to the Cover Date.     

Diamagnetic muonium states in InP

Transverse and zero‐field muon spin relaxation reveal several diamagnetic muonium states in InP characterized by their static linewidths and diffusion properties. We tentatively associate low‐temperature diamagnetic states with Mu⁺ in the BC and T_P interstitial sites and a missing fraction with Mu⁰ rapidly diffusing through T_In interstices. Trapping peaks above 250 K imply static centers which depend on doping type, consistent with Mu^- at T_In for n‐type samples and Mu coupled with a dopant or other defect for p‐type. This revised version was published online in August 2006 with corrections to the Cover Date.     

Interaction of Muons with H2/H3-Centres in Diamond

We report on transverse field muon spin rotation measurements on a nitrogen-rich type Ia diamond, both before and after the conversion of some of the aggregated nitrogen centres to nitrogen-vacancy complexes known as H2/H3-centres. The prompt fractions f and the spin relaxation rates λ were determined for the diamagnetic (μ_d) and the paramagnetic (Mu_T) states in the temperature range 10–300 K. The production of the nitrogen-vacancy complexes had little effect on the parameters of the Mu_T state for which f and λ remained unchanged at approximately 30% and 4 μs⁻¹, respectively. For the μ_d state, on the other hand, the formation of the H2/H3-centres resulted in an increase of the prompt fraction from 10(2)% to 20(3)%, and (for the first time) the spin relaxation rate showed a non-zero value of 0.020(3) μs⁻¹. These results show evidence of strong μ_d interactions with the nitrogen-vacancy complexes in diamond, and suggest a more complex structure for this state than a bare μ⁺. This revised version was published online in September 2006 with corrections to the Cover Date.     

Muonium studies of p-type semi-conducting diamond under conditions of UV-visible illumination

This work reports on the promptly forming fraction and the spin relaxation rate of the isotropic muonium (Mu_T) component in p-type semi-conducting diamond, measured under the condition of illumination. The data are the first such investigations for diamond. A broad band illumination with wavelengths ranging from 0.5 μm to 3 μm was obtained from a Xenon lamp. The energy of the photons was sufficient to excite electrons from the valence band to the 0.28 ppm boron impurity band (0.37 eV). The Transverse Field Muon Spin Rotation (TF-μSR) measurements were conducted as a function of temperature, ranging from 5 K to 300 K. An illumination effect at temperatures below 100 K is observed. It is not yet clear from these data whether the effect is due to Mu_t scattering off delocalized holes, which are removed by illumination or whether there is prompt trapping of Mu_t at boron impurities (passivation) which is affected by illumination. This revised version was published online in August 2006 with corrections to the Cover Date.     

Equivalent states of muonium and implanted hydrogen in silicon (experiment)

Main experimental data on the hydrogen-like states with an anisotropic hyperfine structure forming in silicon single crystals in the implantation of high energy muons and protons are presented. The characteristics of the “anomalous” muonium (Mu^*) and hydrogen-containing silicon AA9 states studied by the muon spin rotation (μSR) and ESR techniques in silicon with a due inclusion of the isotope effect are shown to be similar, thus suggesting the existence of two equivalent structures in silicon, Mu^* and AA9, differing only in the mass of the paramagnetic center.     

Muonium states in semiconductor crystals: Quantum-chemical calculations

The electronic structure of muonium (Mu) located at the bond-centered sites of the silicon and diamond crystals is calculated by the intermediate neglect of differential overlap method. Calculations of the electronicg- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared to the experimental properties of “anomalous” muonium Mu^*. It is shown that the properties of Mu located at the bond-centered sites of the Si and C lattices are in qualitative agreement with the observed properties of Mu^*.     

Muonium centers in heavily n‐doped Si under illumination: Evidence for Mu–hole interaction

A small fraction of implanted muons exists as a paramagnetic state (presumably Mu_BC ⁰, muonium at the Si—Si bond center) in heavily Sb‐doped Si (n-type, [Sb]\ \simeq 10¹⁸\ cm^–3). The paramagnetic state is susceptible to illumination both at 10–20 K and 290 K, providing evidence that holes (minority carriers) play an important role in determining the dynamical properties of muonium centers, where change may occur via a process Mu_BC ⁰+ h⁺\to Mu_BC ⁺ followed by charge exchange reaction (or transition Mu⁺ _BC+ e⁻→ Mu⁰ _T). This revised version was published online in August 2006 with corrections to the Cover Date.     

Final states in Si and GaAs via RF μSR spectroscopy

The ionization of muonium centers in Si and GaAs have been studied using radio frequency (RF) resonant techniques. In Si all three muonic centers are detectable by RF. No evidence was found for delayed Mu and Mu^* states at any temperature. However, our results on the diamagnetic final state (μ _f ⁺ ) show that it is composed of prompt fractions (as seen by conventional μSR) and delayed fractions arising from the ionization of Mu^* and Mu. We observe a full μ _f ⁺ fraction at 317 K when the Mu relaxation rate is above 10 μs⁻¹. GaAs differs from the situation in Si in that we observed only a partial conversion of Mu^* and Mu to a μ⁺ final state up to 310 K in spite of the fact that the transverse field relaxation rates become very high at 150 and 250 K respectively.     

Muon implantation in alkali metal hydrides

Zero, longitudinal and transverse field μSR measurements have been made on LiH, LiD and NaH. The primary motivation for the study was to elucidate the behaviour of the muons in the diamagnetic state and analysis of the time‐dependent zero field relaxation data suggests that negatively charged muonium, Mu^-, is formed and takes up a H^- vacancy site in these materials. Evidence is presented for a small (approximately 2%) reduction in the Mu^-–Li distance relative to the unperturbed nearest neighbour anion‐cation distances in the pure crystal lattices. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hyperfine interactions of muonium and hydrogen in semiconductors: Cluster calculations

The electronic structure of muonium (Mu) located at different interstitial sites of the silicon crystal is calculated by the complete neglect of differential overlap (CNDO) and intermediate neglect of differential overlap (INDO) methods. Calculations of the electronicg- and hyperfine interaction tensors of the impurity atom are performed. The results obtained are compared with the experimental properties of both “normal” (Mu′) and “anomalous” (Mu^*) muonium centers. It is shown that the most likely dynamic model for Mu′ is that in which neutral Mu diffuses rapidly in the silicon lattice, whereas for Mu^* it is the model wherein interstitial Mu is located at the bond-center site. A correlation is made between the characteristics of the hydrogen-bearing Si-AA9 center, recently observed by EPR in a silicon crystal, and those of Mu^*. The Si-AA9 center is shown to be a hydrogen-bearing paramagnetic analogue of the Mu^* center.     

Studies of the positive muon behavior in solid H2 and D2

Using a pulsed muon beam, we have investigated the microscopic μ⁺ behavior in solid H₂ and D₂ down to 0.6 K by the μ⁺SR method. From the studies of μ⁺ spin relaxation phenomena in solid para‐ H₂ and ortho‐ D₂, we have found that μ⁺ forms three distinct microscopic states; H₂μ⁺( D₂μ⁺)(20\sim25\%), muonium (15\sim20\%) and μ⁺(\sim60\%). In H₂μ⁺, the μ⁺ spin is depolarized in solid para‐ H₂ and a local magnetic field B_loc=1\sim2 G is deduced from LF‐μ⁺SR measurements. The magnitude of B_loc is inconsistent with the magnetic dipolar field (\sim25 G) expected from the magnetic moments of two protons in the H₂μ⁺ molecule and suggests that the H₂μ⁺ molecule might be in the rotationally excited state. From LF‐μ⁺SR measurements, muonium and μ⁺ have been found to diffuse in solid o‐ D_2. The diffusion rate of muonium is two order of magnitude larger than that of μ⁺. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mu centers in crystalline Ge under illumination

A slow conversion to a diamagnetic state has been observed for muonium centers at the tetrahedral interstitial site (Mu⁰ _T) in dark Ge at low temperatures. While the conversion process is affected by illumination, no effect of illumination upon the initial (Mu⁰ _T) centers themselves was observed at 10 K. This is in marked contrast with the case of (Mu⁰ _T) centers in Si where strong interaction with photo‐induced carriers is observed, suggesting that the electronic level associated with (Mu⁰ _T) state in Ge is not located in the energy gap. This revised version was published online in August 2006 with corrections to the Cover Date.     

Absolute sign of the Mu* hyperfine parameters in diamond

Standard μSR experiments in diamond have shown that the relative sign of the hyperfine parameters of the anisotropic Mu^* state is negative (A _‖/A _⊥<0). We report an experimental determination of theabsolute sign of the Mu^* hyperfine parameters by studying the transferred muon polarization during the thermally-activated transition from the isotropic Mu state to Mu^*. The results demonstrate that the isotropic part of the Mu^* hyperfine interaction is negative. In a nitrogen-poor diamond, both the Mu disappearance rate and the enhancement of the Mu^* signals are well-described by a single Arrhenius law.     

Electronic properties of HfXY intermetallic compounds (X = Si, Ge; Y = S, Se, Te)

Muonium, with a positive muon as the nucleus is considered a light isotope of hydrogen displaying a close chemical analogy to this atom. It offers a unique opportunity to study the behaviour of hydrogen in diamond at very low concentrations. The mass difference, however, implies that dynamical effects will be distinct. The bond centred muonium (Mu _BC ) state in diamond is easily observed and there is a very good correlation between theoretical and experimental hyperfine parameters (Schneider et al., Phys. Rev. Lett. 71(4):557–560, 1993). Curiously, despite its predicted stability, the bond centred hydrogen state has not yet been observed in diamond. Following the discovery of hydrogen dopant states in certain wide band gap metal oxides, and the possibility of hydrogen related molecular dopants in diamond, the study of hydrogen in diamond is important. Although it is evident from its hyperfine parameters that Mu _BC is not a shallow donor, the question still arises as to where the Mu _BC state in diamond might lie in the band gap. Accordingly, measurements of the high temperature stability of Mu _BC have been performed in a search for its possible ionization. The results are consistent with such an ionization, as the disappearance of Mu _BC polarisation (setting in near 1000 K) is correlated with the slight increase in the population of the diamagnetic μ⁺ species.     

Longitudinal field muon spin relaxation (LF-μSR) measurements and evidence for a new muonium defect site in type Ia diamond

A new configuration for muonium, with hyperfine interaction parameters of less than axial symmetry, in nitrogen rich diamond is identified in Longitudinal Field Muon Spin Relaxation (LF-μSR) measurements. The TF-μSR measurements on the same sample show that almost the entire strength of the new configuration is accounted for by a “missing fraction”, typically seen in nitrogen rich type Ia diamond. The “missing fraction” is therefore the result of a T2 relaxation. This is consistent with muon trapping at or in some nitrogen related defect(s) followed by electron capture at random times. This revised version was published online in August 2006 with corrections to the Cover Date.     

High‐pressure μSR studies of ferro‐ and antiferromagnetic metals

High‐pressure μSR experiments on ferromagnetic nickel and \alpha‐iron and antiferromagnetic chromium are reported. In Ni above 260 K B_Fermi was found to be proportional to the saturation magnetization, whereas at lower temperatures it is temperature independent apart from a small anomaly below 30 K which is presumably caused by a magnetoelastic interaction. There was no evidence for an occupation of metastable sites by the μ⁺ below the Curie temperature. By contrast, in \alpha‐Fe the temperature dependence of \curpartialB_μ/\curpartialp shows a structure which might be attributed to the occupation of excited muon states at elevated temperatures. High‐pressure zero‐field experiments on Cr performed in the temperature regime between 4.5 K and 8 K revealed a pressure dependence of B_μ as large as \curpartialB_μ/\curpartialp=-(89.15\pm 0.06)\times 10^-12 T/Pa. In terms of volume dependence a very large negative Grüneisen parameter \gamma =-27 was obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Interaction of muonium with oxygen on silica powder surfaces

Results of the first μSR studies using Merck FO Optipur silica powder, which contains paramagnetic impurities at the ppb level and has a surface area of 610±20 m²/g. are reported. Above 20 K, the transverse field muonium relaxation rate is roughly constant at 0.5 μs⁻¹. Upon the addition of oxygen at ppm levels, the relaxation rate increases linearly with O₂ concentration in the temperature range from 40–100 K yielding two-dimensional depolarization rate constants on the order of 10⁻⁴ cm² molecule⁻¹ s⁻¹. As the temperature is increased further, both oxygen and muonium desorb from the surface yielding a three-dimensional rate constants at 300 K of 3.1(3)×10–10⁻¹⁰ cm³ molecule⁻¹ s⁻¹, in agreement with the gas phase value. Longitudinal field measurements suggest that MuO₂ is formed and is able to spin exchange with other oxygen molecules.     

Muon spin rotation experiments on a silicon crystal doped with13C

A crystal of silicon doped with carbon enriched to 60.1% in¹³C was studied bySR to determine whether¹³C hyperfine structure could be observed in the frequency spectra of normal muonium, Mu, or anomalous muonium, Mu^*. Measurements at 100 G and 100 K with 40 million good events yielded extremely weak Mu^* signals and no Mu in these data or in measurements at 10 G and 150 K. Transmission electron micrographs of this sample contained small regions showing strain contrast and structure factor contrast. Annealing the sample at 900°C for 84 hours led to featureless electromicrographs. SubsequentSR measurements yielded a strong Mu^* signal but still no Mu. No broadening due to¹³C was observed.